Problems on Numbers · Exercise 4 of 6
65 mixed-level problems on numbers in the style of campus placement tests (TCS, Infosys, Wipro, Accenture, Cognizant, Capgemini), SSC CGL/CHSL/MTS, RRB NTPC and Group D, IBPS/SBI, UPSC CSAT and state exams.
If three-fourths of a number is 27, what is two-thirds of the number?
3x/4 = 27 → x = 36
Two-thirds of 36 = 24
Answer: 24
When a number is divided by 4 and by 5, the two quotients differ by 3. What is the number?
x/4 − x/5 = 3
(5x − 4x)/20 = 3
x = 60
Answer: 60
What is the largest odd two-digit number whose digits add up to 7?
Two-digit numbers with digit sum 7: 16, 25, 34, 43, 52, 61, 70
Odd ones: 25, 43, 61
Largest = 61
Answer: 61
A person thinks of a number, multiplies it by 4, adds 8, divides the result by 2 and then subtracts 4. The answer is 30. What number did he think of?
(4x + 8)/2 − 4 = 2x + 4 − 4 = 2x
2x = 30
x = 15
Answer: 15
If n is a natural number such that n² + n = 650, what is n?
n(n + 1) = 650
√650 ≈ 25.5 → try 25 × 26 = 650 ✔
n = 25
Answer: 25
A two-digit number has 4 as its tens digit and is exactly 9 times its units digit. What is the number?
Number = 40 + b
40 + b = 9b
8b = 40 → b = 5
Number = 45
Answer: 45
20% of one number equals 30% of another, and the two numbers add up to 150. What is the smaller number?
0.2a = 0.3b → a : b = 3 : 2
Smaller = 150 × 2/5 = 60
Answer: 60
When a number is doubled and 5 is added, the result is 3 more than three times the number. What is the number?
2x + 5 = 3x + 3
x = 2
Answer: 2
Three numbers are in the ratio 2 : 3 : 5 and the sum of their squares is 608. What is the largest number?
Let the numbers be 2k, 3k, 5k.
4k² + 9k² + 25k² = 38k² = 608 → k² = 16 → k = 4
Largest = 5 × 4 = 20
Answer: 20
When 35 is subtracted from a number, it reduces to 80% of itself. What is four-fifths of the number?
x − 35 = 0.8x → 0.2x = 35 → x = 175
Four-fifths of 175 = 140
Answer: 140
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